Question

Vacancies of the crystal may arise due to:

• A. thermal vibrations
• B. optical vibrations
• C. quantum vibrations
• D. vacuum fluctuations

Hint:

Remember that the concentration of vacancies in a material is highly dependent on temperature, following an Arrhenius-type equation: \( N_v = N \exp(-E_v / k_B T) \), where \(E_v\) is the vacancy formation energy. This directly links vacancies to thermal energy.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A vacancy is a type of point defect in a crystal where an atom is missing from one of the lattice sites. The question asks for the primary cause of the formation of these vacancies.
Step 2: Detailed Explanation:
The formation of vacancies is a thermodynamically driven process. In any crystal at a temperature above absolute zero (0 K), the atoms are not stationary but are constantly vibrating about their equilibrium positions. These vibrations are called thermal vibrations.
As the temperature increases, the amplitude of these thermal vibrations increases. Occasionally, an atom on a lattice site may gain enough thermal energy from its neighbors to overcome the bonding forces holding it in place. This atom can then jump out of its site and move to the crystal's surface or an interstitial position, leaving behind an empty lattice site—a vacancy.
The equilibrium number of vacancies increases exponentially with temperature. The other options are not the primary cause:


Optical vibrations: These are a mode of lattice vibration but 'thermal vibrations' is the broader and more direct cause related to temperature and energy fluctuations that create vacancies.
Quantum vibrations (zero-point energy): While atoms do vibrate even at 0 K due to quantum mechanics, this energy is generally not sufficient to create a significant number of vacancies.
Vacuum fluctuations: This is a concept from quantum field theory and is not relevant to the formation of vacancies in a solid crystal lattice.
Step 3: Final Answer:
The primary reason for the creation of vacancies in a crystal is the random thermal energy associated with atomic vibrations, i.e., thermal vibrations.